Let a1 = 1 and an = n(an-1 + 1 ) for n=2,3,.....
P = (1+ 1/a1 )(1+1/a2)......(1+1/an )
The Limit P when n tends to infinity is?
Now see if you can turn those observations into proofs. You need to show first that the product is equal to . Then you want to show that .
Hint for that last part: let . Show that , and deduce that .